Out in the Gulf BP are going through the preparations for the next stage in the attempt to top kill the deep water well that has been leaking oil and gas for more than a month. The kill attempt has now been underway for a couple of days, and so this is initially a recap on what I believe has happened to date, and what they are currently planning on doing. I will include in this explanation the two attempts that BP have made so far, and what I expect that they will do next.



To help with the explanation I am going to use some very simple models, which oversimplify the situation, but hopefully will help explain it. To start with I am going to break the overall system down into a very simple diagram.



Basically BP are sending mud through a series of feed lines, which I have simplified for the explanation into one feed pipe that I have called the choke line (grey). It has an internal diameter of, at most, of 3 inches. (I say "at most" because most fittings on these lines have smaller diameters). It feeds into the top of the well, which I have colored brass, and which is the pipe (casing) that feeds from the seabed down to where the oil is emerging from the rock, some 13,000 ft further down.



The casing and choke line sit underneath the Blowout preventer (which is the large assembly at the top of the rig). I have colored this bronze, and simplified the shape, for this explanation, to represent a pipe that has been partially closed by the action of the BOP.



Now, here is the problem. BP want to feed mud through the choke line at such a pressure and flow that it will push the oil and gas flowing up out of the well back down the well. To do that they have to create enough resistance to the flow that the combination of the mud flow and the oil can’t all escape out through the hole in the BOP.



They can do this since, as you increase the flow through a hole (or nozzle), it has to move faster to get through the space in a given time. It takes a driving pressure to get the fluid moving at that speed, and for a given driving pressure the fluid will only move at a certain speed, and so only a fixed volume of fluid can go through the hole.



Thus if BP pump more fluid into the well than this volume, for that given pressure (which is higher than the pressure that the oil was flowing at) then all the flow out of the well will change to mud, and the excess mud that is not flowing out of the hole will be at enough pressure over the oil (and gas) in the well that it pushes it back down the well and back into the rock.



Now that was the first step. The idea was that once the column of mud filled the well, down to where the rock reservoir lies, that the weight of the mud would exert a pressure on the oil in the rock, that was higher than the fluid pressure, and the flow would stop.



The first time they did this, the density of the mud (weight of a cubic foot) was not high enough for the full column to balance the pressure in the rock, and the leakage of mud out of the hole in the top of the BOP was higher than BP had thought, so they were losing too much mud to the Gulf.



So they moved to step two. The first part of this is to try to reduce the size of the hole in the BOP. And for this they used a variety of what everyone is calling a junk shot. It actually isn’t. Given the problem that I am about to outline, they have an ally that folks normally don’t have. As Secretary Chu has pointed out there is the full intellectual strength of the Federal Labs behind this attempt, so where one would normally just chop up tires and similar materials, there is a fascinating mathematical problem in designing plug pieces of the right shape that will fit the constraints, and which will accelerate the blocking of the flow path. So I suspect that some of the shapes that will appear in the flow will have been specificially designed for the problem.



Not being familiar with their answer I’m going to stick with the spheres and triangles of the more traditional, shall we say old fashioned, way of addressing the problem.



It is one of these problems where the bounding conditions can make life rather difficult. Let me redraw the problem with a different orientation. What we have to do is to block (the term that is being used is bridge) the passage through the BOP. This will stabilize the flow, and will allow the cement plug time to set up. (We’ll talk about cements another time).



So here is the slit: through the BOP – it is going to be a more complex shape, but this allows some explanation of the problems.

Now to block the slot we have to have some pieces of material (although they are quite large for simplicity I am going to call them all particles) that are big enough to wedge in the slot, but small enough to get through the feed lines to that point.



Now here’s the first catch, we don’t want them to be hard enough that we will damage the passages, nor soft enough that they will bend distort and compress and squeeze through the hole. Rubber turns out to fit the bill, and though there are other materials that could be better, in this initial explanation that’s what I am going to use.



The easy thing to do is to use some spheres, not easy to get, though golf balls are an example. Unfortunately they are a bit too big. The reason is that the feed line through the choke has a maximum inner tube size of probably 2.75 inches. A golf ball is about 1.6 inches, which is more than half this, so that two balls together could block the feed line – a definite no-no. (And don’t say it can’t happen, I’ve seen it with smaller particle ratios than this).